Since the 1967-68 season the Leafs have beaten the following ten teams:
Los Angeles (1974-75, 1977-78), Pittsburgh (1975-76, 1976-77, 1998-99), the Islanders (1977-78, 2001-02), Atlanta (1978-79), Chicago (1985-86, 1993-94), St. Louis (1986-87, 1992-93), Detroit (1992-93), San Jose (1993-94), Philadelphia (1998-99), and Ottawa (1999-00, 2000-01, 2001-02, 2003-04).
Detroit has beaten the following twenty different teams:
Atlanta (1977-78), Chicago (1986-87, 1994-95, 2008-09), Toronto (1986-87, 1987-88), St. Louis (1987-88, 1995-96, 1996-97, 1997-98, 2001-02), Minnesota (1991-92), Dallas (1994-95, 1997-98, 2007-08), San Jose (1994-95, 2006-07), Winnipeg (1995-96), Anaheim (1996-97, 1998-99, 2008-09), Colorado (1996-97, 2001-02, 2007-08), Philadelphia (1996-97), Phoenix (1997-98, 2009-10), Washington (1997-98), Los Angeles (1999-00), Vancouver (2001-02), Carolina (2001-02), Nashville (2003-04, 2007-08), Calgary (2006-07), Pittsburgh (2007-08), and Columbus (2008-09).
Chicago has beaten the following thirteen different teams:
New York Rangers (1967-68, 1970-71, 1972-73), Detroit (1969-70, 1984-85, 1988-89, 1991-92), Philadelphia (1970-71), Pittsburgh (1971-72), St. Louis (1972-73, 1979-80, 1981-82, 1982-83, 1988-89, 1989-90, 1991-92), Los Angeles (1973-74), Boston (1974-75), Minnesota (1981-82, 1982-83, 1984-85, 1989-90), Edmonton (1991-92), Toronto (1994-95), Vancouver (1994-95, 2008-09), Calgary (1995-96, 2008-09), and Nashville (2009-10).
I'm guessing that the team you're looking for is Detroit. Twenty different teams, or a full two-thirds of the league, is just ridiculous. Montreal beat a lot of the same teams over the years when they were in their heyday but if you can wait a moment I will go check.
Edit: Montreal has beaten the following seventeen different teams since the 1967-68 season:
Boston (1967-68, 1968-69, 1970-71, 1976-77, 1977-78, 1978-79, 1983-84, 1984-85, 1985-86, 1986-87, 1988-89, 2001-02, 2003-04, 2007-08), Chicago (1967-68, 1970-71, 1972-73, 1975-76), St. Louis (1967-68, 1968-69, 1976-77), New York Rangers (1968-69, 1978-79, 1985-86), Minnesota (1970-71), Buffalo (1972-73, 1989-90, 1990-91, 1992-93), Philadelphia (1972-73, 1975-76, 1988-89), Vancouver (1974-75), New York Islanders (1975-76, 1976-77, 1992-93), Detroit (1977-78), Toronto (1977-78, 1978-79), Hartford (1979-80, 1985-86, 1987-88, 1991-92), Quebec (1983-84, 1986-87, 1988-89, 1992-93), Calgary (1985-86), Los Angeles (1992-93), Pittsburgh (1997-98), Washington (2009-10).